Recent advances in sensor technology and information processing afford a new flexibility in the design of waveforms for agile sensing. Sensors are now developed with the ability to dynamically choose their transmit or receive waveforms in order to optimize an objective cost function. This has exposed a new paradigm of significant performance improvements in active sensing: dynamic waveform adaptation to environment conditions, target structures, or information features. The manuscript provides a review of recent advances in waveform-agile sensing for target tracking applications. A dynamic waveform selection and configuration scheme is developed for two active sensors that track one or multiple mobile targets. A detailed description of two sequential Monte Carlo algorithms for agile tracking are presented, together with relevant Matlab code and simulation studies, to demonstrate the benefits of dynamic waveform adaptation. The work will be of interest not only to practitioners of radar and sonar, but also other applications where waveforms can be dynamically designed, such as communications and biosensing.